There are a variety of waves in plasma depending on how electron current is
generated with electric and magnetic fields. In general, we can separate the type of
such waves to two, namely, the transverse waves and longitudinal waves. They are
defined by the following relations:
Transverse waves: ∇ Á E ¼ 0
Longitudinal waves: ∇ Â E ¼ 0
In the case of small amplitude electric and magnetic fields of the waves, we can
expand the physical quantities in Fourier-Laplace components which allow to
assume the space and time dependence of the quantities in the complex form pulse
its complex conjugate:
E t, r
ð Þ /
X
k, ω
E k, ω
ð
Þe
ÀiωtþkÁr
þ c:c:
ð2:2:9Þ
In (2.2.9), ω and k are the angular frequency and wavenumber vector,
respectively.
In what follows, the complex expression is used for convenience of mathematics,
and the real values can be obtained by taking the real components of the resultant
physical quantities or assuming all components are the sum with its complex
conjugate as shown in (2.2.9). In the form of (2.2.9), the transverse and longitudinal
waves are characterized as shown in Fig. 2.7a and b. The vector k is the direction of
the wave propagation, and the transverse waves have the electric field perpendicular
k
E
B
k
E
B=0
Fig. 2.7 Geometrical
relation for plane waves: (a)
electromagnetic waves and
(b) electrostatic waves. The
electric field is stronger in
Lorentz force than magnetic
force in non-relativistic
regime, and the
wavenumber k is
perpendicular to the electric
field in (a), while it is
parallel in (b). The
electromagnetic waves have
no density perturbation in
plasmas, while the
electrostatic waves are
maintained by the electric
field due to the charge
separation of electrons from
the ions
42
2 Laser Absorption by Coulomb Collision